In the bowl of a stand mixer fitted with a paddle attachment (see headnote if you don’t have one), mix together the eggs, sourdough discard, pumpkin purée, and peanut butter until combined.

Mix in the oats and leave to rest at room temperature for 30 minutes, allowing the oats to absorb some of the liquid, or until the mixture resembles a loose cake batter.

Heat the oven to 350°F.

Add 1½ cups of the whole-wheat flour to the wet ingredients, mixing on low speed until incorporated. If the mixture is still very sticky, add the remaining flour in ¼-cup increments until you have a lightly tacky dough that clears the side of the bowl.

Transfer the dough to a lightly floured surface and knead a few times just to bring everything together.

Divide the dough in half. Dusting with flour as needed to prevent sticking, roll out the dough into a ¼-inch-thick sheet. Cut the treats into your desired shape using a 1- to 2-inch cookie cutter. Alternatively, use a sharp knife or pizza cutter to cut the dough into 1- to 2-inch squares. Transfer the treats to a parchment-lined baking sheet. The treats will not expand during baking, so you can place them pretty close together. Repeat with the remaining dough.

Bake the treats for 20 minutes, until puffed and slightly browned. These treats are on the chewy side; if your dog prefers something crunchier, bake for an additional 10 minutes. Let cool, then go find your dog to see how popular you are.